(1) Field of the Invention
The present invention is directed to acoustic vector sensors. In particular, the present invention is directed to increasing the directionality of a sensor having a size much less than the wave length of an acoustic wave, by measuring the acoustic fluctuations of fluid density at a point.
(2) Description of the Prior Art
Conventional vector sensors measure particle velocity, v (vx, vy, vz), associated with an acoustic wave. The measurements of a vector quantity (velocity) instead of a scalar quantity (pressure) allows for directional sensing even if the size of the vector sensor is much smaller than the size of the wavelength of the acoustic wave. The directionality pattern of a vector sensor is proportional to cos(θ), where θ is the directional angle of the vector sensor. Vector sensor directionality is equivalent to the dipole-type or first order sensor that is realized by measuring particle velocity at a point, (which is the vector sensor sensing approach for underwater sensors), or by measuring the gradient of the acoustic pressure at two closely spaced (less than the wavelength of an acoustic wave) points as it is commonly done in air acoustics where this type of sensor is called an acoustic intensity probe. The two approaches of obtaining vector sensor directionality as described above are in fact mathematically equivalent according to a linearized equation of momentum conservation as expressed in Eq. (1) below:
                              ρ          0                =                                                            ∂                v                                            ∂                t                                      +                          ▽              ⁢                                                          ⁢              p                                =          0                                    (        1        )            Here ρ0 is the undisturbed fluid density and is the ∇p gradient of the acoustic pressure. For a plane wave propagating in the x-direction Eq. (1) can be re-written as Eq. (2) below:
                                          ρ            0                    ⁢                                    ∂              v                                      ∂              t                                      =                  -                                    ∂              p                                      ∂              x                                                          (        2        )            
There continues to be a need to increase the directionality of a vector sensor. One approach to further increase the directionality of a vector sensor while still maintaining a sensor size that is much smaller than the wavelength of an acoustic wave, is to utilize a second order or quadruple-type sensor arrangement measuring the diversion of the velocity, div v. This can be accomplished by measuring the components of the velocity, v (vx, vy, vz), at closely spaced points (at least two points) along the corresponding axis yielding the directionality, which is proportional to cos2(θ). The benefit of the increased directionality, however, when measured using this approach comes at a cost of the number of vector sensors necessary and at a cost of a reduction in sensitivity. Two vector sensors for each axis (a minimum of six sensors) are required to measure the diversion of the velocity and there is a significant reduction in sensor sensitivity proportional to kd<<1, where k is the wave-number and d is the spacing between the two vector sensors.
A more advantageous means to achieve a second order directionality is to measure the acoustic fluctuations of fluid density at a point rather than directly measuring the diversion of the velocity.